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 \begin{table}[htbp] 
  \caption{\bf Pricing Ability:  local-PCA vs constant-PCA  - SDF ($T=24$)}
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\begin{tabular}{lccccccccccc}
  \multicolumn{12}{c}{\bf Pricing Ability:  SDF }   \\  \hline 
  Out-of-Sample   &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
 \scriptsize{  constant-PCA/local-PCA (bal)} &    3.262  & 27.791 &  9.503 &  8.116 &  4.875 &  3.106 &  2.302 &  1.871 &  1.323 &   0.915 &   0.712  \\
 \scriptsize{  constant-PCA/local-PCA (unb)}  &  1.096  & 5.416 &  3.003 &  1.776 &  3.329 &  4.38 &  1.745 &  1.468 &  0.581 & 0.864  & 0.721 \\  \hline
In-Sample  &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
 \scriptsize{  constant-PCA/local-PCA (bal)} &   1.870 & 12.83 & 4.475 &   3.213 &   2.198 &   1.683 &   1.323 &   1.089 &   0.889 &   0.740 &   0.613 \\
 \scriptsize{  constant-PCA/local-PCA (unb)} &   0.849 & 3.510 &  2.079 & 1.533 &  1.082 & 0.804 & 0.633 & 0.513 & 0.429 & 0.365  &  0.298  \\
 \multicolumn{12}{c}{\bf Pricing Ability:  Risk Premia }   \\  \hline
 Out-of-Sample   &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
 \scriptsize{  constant-PCA/local-PCA (bal)} 
 & 0.845 &
 10.470  & 6.567 & 4.784 & 3.674  & 2.927  & 2.369 & 1.955  & 1.631  & 1.375 &  1.169 \\
  \scriptsize{  constant-PCA/local-PCA (unb)} & 1.492 &
  5.534  & 3.407  & 2.461  & 1.880 & 1.493 & 1.205  & 0.992  & 0.827  & 0.697 & 0.592  \\ \hline
 In-Sample &  $\tilde{r} $ & $1$  &  $ 2 $ & $3$ & $4$ & $5$ & $ 6 $ & $7$   & $8$  & $9$ &  $10$ \\   \hline
  \scriptsize{  constant-PCA/local-PCA (bal)} &   4.634 &  23.767 &   8.151  &   6.337  &   5.0468 &   3.550 &   3.720 &   2.465  &   2.660 &  2.420  &   1.738  \\ 
  \scriptsize{  constant-PCA/local-PCA (unb)} &   2.908  & 161.306  &  10.825  &   5.052 &    3.246  &   3.148  &   3.210  &   2.094  &    1.455 &  1.280  &    1.330 \\ \hline   
    \end{tabular}
        \parbox{7.0in}{\footnotesize{Each entry  represents the ratio between the pricing statistics for the constant-PCA over the local-PCA for both the balanced \newline (bal) and unbalanced (unb) panel case:  ratios (in absolute value)  of  the time-averages (across $480-2T$ windows) of the \newline  bias-adjusted
  SDF pricing statistics $ N^{-1}  \sum_{i=1}^N \tilde{ h}_{i}^2  $  (top two panels)     
        and of the  bias-adjusted
 risk premia pricing \newline statistics  $ N^{-1} \sum_{i=1}^N \tilde{ \delta}_{i}^2  $
          (bottom two panels), both described in Theorem~3. %\ref{Ttest}.
        Panels two and four report the in-sample results \newline and panels one and three report the  out-of-sample  results,
    correspondingly to  the  estimated $\tilde{r}$   (column two), described in \newline Section~OA15.1, %\ref{EAOATV},  
    and fixed risk factors ranging from one to   $ 10 $ (columns three-12), respectively
     (monthly data Jan-1980 \newline to Dec-2019,  $T=24$, $N = 19,259$, sourced from CRSP.}}
\label{Table2}
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